The present invention relates to membrane-based filtration systems and more particularly to techniques for optimizing the operation of such systems to maximize recovery of a desired component in minimum time.
Filtration systems commonly used in industrial applications today include tangential flow filtration (TFF) systems which use membranes to separate components in a liquid sample solution on the basis of their effective size differences. The sample solution housed in a tank or other suitable reservoir flows across the face of the membrane at an elevated pressure which drives permeable components smaller than the pore size of the membrane through the membrane as permeate while retaining larger components in a retentate stream. The retentate stream is recirculated to the tank and ultimately pumped across the membrane in a continuous fashion. Notwithstanding the sweeping flow action of TFF systems, certain component species within the sample solution typically remain trapped on the surface of the membrane and form a concentration polarization gradient which affects the permeability of those components passing through the membrane.
Depending on the mode of operation of the TFF system, the volume of the sample solution can be significantly reduced as permeate is withdrawn from the system as the sample solution becomes concentrated (i.e. concentration mode). On the other hand, many applications involving the separation of two or more components add a diafiltrate solution at the same rate as permeate is withdrawn to maintain the overall system volume constant while removing the permeable component from the sample solution (i.e. constant volume diafiltration mode). Control strategies also can involve combinations of concentration and diafiltration modes of operation. These strategies involve control of both the diafiltrate flow (q.sub.d) and the permeate flow (q.sub.p). There have been numerous attempts published in the literature to try to optimize processing conditions by controlling certain parameters of the TFF system.
As described by Blatt et al., Anal. Biochem., 26 (1968) 151, discontinuous batch diafiltration involves varying the diafiltrate flow rate from a pure concentration mode (q.sub.d =0) to a pure dilution mode (q.sub.p =0) in a step wise manner. This process is repeated as a series of n sequential concentrations (from volume V.sub.O to volume V) and dilutions where system concentrations decline from an initial value c.sub.O to a value c=c.sub.0 (V.sub.0 /V).sup.-.sigma.n for component passage .sigma.. However, as subsequently recognized (see Ch. 3 in Mears, "Membrane Separation Processes", 1976) the discontinuous diafiltration method produces lower average fluxes due to the higher average system concentrations of the polarizing species over the diafiltration process. This will require long processing times or large system membrane areas to reach the target purity. Additionally, discontinuous diafiltration is cumbersome to implement in a production scale system.
As described in the same publication as above, Blatt et al. also refer to constant volume batch diafiltration which involves keeping the diafiltrate flow rate equal to the permeate flow rate over the entire process. This maintains a constant system fluid volume V.sub.O during the process while component concentrations in the system decline from an initial value of c.sub.0 to a value c=c.sub.0 e.sup.-.sigma.V.sbsp.d.sup./V.sbsp.o for component passage .sigma. and diafiltrate volume V.sub.d. While high fluxes can be maintained using this technique, the large amount of diafiltrate required can result in long process times or large membrane areas, both of which lead to uneconomical results.
A modification of constant volume batch diafiltration was described by Ng et al., Sep. Sci., 11, (1976) 499. In this scheme, initial experimental data is generated to produce a plot of flux versus concentration of the polarizing species. The optimum diafiltration point (c.sub.g /e) is determined by first extrapolating the generated data points to find the zero flux intercept or gel point (c.sub.g) and then dividing by 2.718 (the value of e). After c.sub.g /e is determined, implementation of the control strategy occurs in two steps, first by conducting either a pure concentration mode (q.sub.d =0) step or pure dilution mode (q.sub.p =0) step to bring the concentration of the polarizing species from its initial value c.sub.o to c.sub.g /e. The next step is to run the system under constant volume diafiltration conditions at this empirically obtained optimized polarizing species concentration point until the desired retentate concentration of the passing species is obtained.
The existence of an optimum diafiltration concentration according to the teachings of Ng et al. arises from a tradeoff between the decreasing volume of permeate produced as one concentrates the initial batch, and the decreasing flux produced as the concentration of retained components are increased. The N get al. strategy is economically optimal when the diafiltration step process time dominates the total process time, the polarizing species is completely retained, the passage of the permeating species is constant, and the flux (J) variation with the concentration of the polarizing species (c) is described by the film model as J=k ln (c.sub.g /c). In this model, c.sub.g is the gel point and k represents the mass transfer coefficient. The foregoing conditions are not always met over the wide range of variables typical of most TFF applications.
Beaton and Klinkowski, J. Sep. Proc. Techn., 4 (1983) 1, use the same strategy as Ng et al. but account for deviations in flux (J) from the film model. They identify the optimum batch concentration of the polarizing species (c) at which to diafilter as that value of (c) which produces a minimum in the plot of 1/Jc vs c. While this publication recognizes in some cases that flux varies with both the retained species concentration and the permeating species concentration, the authors suggest using the Ng et al. diafiltration strategy with a flux versus polarizing species relationship, J(c), which is determined at low permeating species concentrations. Hence this technique ignores the flux dependence on the permeating species and thus will not produce optimum results when the flux varies over the course of the diafiltration.
Jaffrin et al., Recents Progres Genie Procedes, 6 (1992) 299, considered the effect of both retained species concentration and permeating species concentration on flux by adding another step to the Ng et al. strategy for an application involving the removal of ethanol from albumin. The feed is first diluted with water to reduce ethanol concentration, then concentrated to increase the albumin concentration. After these steps, a constant volume diafiltration was run to reduce ethanol concentration to a final specification. The Jaffrin et al. step-wise process is a discontinuous approximation of actual conditions and thus does not accurately reflect optimal system operations. This publication also hints at a possible different strategy involving diafiltration under diminishing volume. However, no analysis or data is shown as to how one might implement this approach. More recently, Jaffrin et al., J. Mem. Sci. 97 (1994) 71, elaborate on the above strategy by describing operation at a constant diafiltrate to permeate flow ratio over the entire process. The "trial and error" optimization strategy used to identify the best value for this ratio provides little guidance as to when this approach has utility. In addition by requiring a fixed ratio over the entire process, this strategy does not account for the effect of changing concentrations of the species.
DiLeo et al., U.S. Pat. No. 4,728,430, described the first significant departure from the Ng et al. strategy by proposing a new diafiltration processing technique based on maintaining a constant system concentration of a particular polarizing species instead of maintaining a constant volume. This strategy allows for the case where the polarizing species is only partially retained by specifying a diafiltrate addition flow where the system volume decreases over the course of processing. While this strategy is described in the context of blood plasma separation, it is generally applicable to all separations using TFF where only one particular component controls the flux and passage over the course of processing.
All of the foregoing attempts have failed to adequately take into account when more than one species in the sample to be filtered controls the flux and passage of the permeating species during diafiltration and thus are deficient in the processing goal of maximizing recovery of the desired component in the minimum amount of time.